The Gettier problem is considered a problem in modern epistemology issuing from counter-examples to the definition of knowledge as justified true belief (JTB). The problem owes its name to a three-page paper published in 1963, by Edmund Gettier, called "Is Justified True Belief Knowledge?", in which Gettier argues that this is not necessarily the case. Many or most analytic philosophers would wish to be able to hold to what is known as the JTB account of knowledge: the claim that knowledge can be conceptually analyzed as justified true belief — which is to say that the meaning of sentences such as "Smith knows that it rained today" can be given with the following set of necessary and jointly sufficient conditions:

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Gettier's paper used counterexamples (see also Thought experiment) to argue that there are cases of beliefs that are both true and justified — therefore satisfying all three conditions for knowledge on the JTB account — but that do not appear to be genuine cases of knowledge. Gettier, therefore, argued that his counterexamples show that the JTB account of knowledge is false — and thus, that a different conceptual analysis is needed to correctly track what we mean by "knowledge".

Gettier's case is based on two counterexamples to the JTB analysis. Both of them rely on the established claim (under JTB) that justification is preserved by entailment, and the further claim that such applies significantly, or can be applied there coherently to the "stipulation" attributed to Smith's putative "belief" in the case of this particular counter-example: that is, that if Smith is justified in believing P, and Smith realizes that the truth of P entails the truth of Q, then Smith would also be justified in believing Q. Gettier calls these counterexamples "Case I" and "Case II":

Smith has applied for a job, but, it is claimed, has a justified belief that "Jones will get the job". He also has a justified belief that "Jones has 10 coins in his pocket". Smith therefore (justifiably) concludes (by the rule of the transitivity of identity) that "the man who will get the job has 10 coins in his pocket".

In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.

Smith, it is claimed by the hidden interlocutor, has a justified belief that "Jones owns a Ford". Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown.

In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Again, Smith had a belief that was true and justified, but not knowledge.

In both of Gettier's actual examples,
(see also counterfactual conditional), the justified true belief came about, if Smith's purported claims are disputable, as the result of entailment (but see also material conditional) from justified false beliefs, namely, that "Jones will get the job" (in case I), and that "Jones owns a Ford" (in case II). This led some early responses to Gettier to conclude that the definition of knowledge could be easily adjusted, so that knowledge was justified true belief that depends on no false premises.

The "no false premises" (or "no false lemmas") solution which was proposed early in the discussion did not settle the matter, as more general Gettier-style problems were then constructed or contrived, in which the justified true belief does not seem to be the result of a chain of reasoning from a justified false belief.

For example:

After arranging to meet with Mark for help with homework, Luke arrives at the appointed time and place. Walking into Mark's office Luke clearly sees Mark at his desk; Luke immediately forms the belief 'Mark is in the room. He can help me with my logic homework'. Luke is justified in his belief; he clearly sees Mark at his desk. In fact, it's not Mark that Luke saw; it was a marvelous hologram, perfect in every respect, giving the appearance of Mark diligently grading papers at his desk. Nevertheless, Mark is in the room; he is crouched under his desk reading Frege. Luke's belief that Mark is in the room is true (he is in the room, under his desk) and justified (Mark's hologram is giving the appearance of Mark hard at work).

Again, it seems as though Luke does not "know" that Mark is in the room, even though it is claimed he has a justified true belief that Mark is in the room, but it's not nearly so clear that the perceptual belief that "Mark is in the room" was inferred from any premises at all, let alone any false ones, nor led to significant conclusions on its own; Luke didn't seem to be reasoning about anything; "Mark is in the room" seems to have been part of what he seemed to see.

To save the "no false lemmas" solution, one must logically say that Luke's inference from sensory data does not count as a justified belief unless he consciously or unconsciously considers the possibilities of deception and self-deception. A justified version of Luke's thought process, by that logic, might go like this:

And the third step counts as a false premise. But by the previous argument, this suggests we have fewer justified beliefs than we think we do.

In another example, Matthew drives through an area that appears to have many barns. In fact it contains a great many realistic barn facades, perhaps made to help shoot a Hollywood movie 'on location'. When Matthew looks at the one real barn along his route, he forms the allegedly justified true belief, 'There's a barn over there.' But if he follows the strong requirement for justified belief, then his thought process will follow the previous mentioned steps exactly. A similar process appears in Robert Heinlein's Stranger in a Strange Land as an example of "Fair Witness" behavior.

The Gettier problem is posed in terms of a problem in first-order logic, but the introduction into the discussion by Gettier of terms such as belief and knows moves the discussion into the field of epistemology. Here, the sound (believed) arguments ascribed to Smith, then need also to be valid (true) and convincing (justified) if they are to issue in real-world discussion about justified true belief.
[1]
Gettier's problem has attracted a range of more sophisticated responses. The different directions that these responses have taken are constrained by the structure of Gettier's argument: if knowledge is solely justified true belief, then there cannot be any cases of justified true belief that are not also cases of knowledge; but Gettier claims that his counterexamples are cases of justified true belief without being cases of knowledge. Therefore, in this account, one is to either accept Gettier's conclusion — and elucidate a new conceptual analysis for knowledge — or else deny one of Gettier's two claims about his counterexamples (that is, either deny that Gettier cases are justified true beliefs, or else accept that Gettier cases are knowledge after all).

One response, therefore, is that in none of the above cases was the belief justified: it is impossible to justify anything which is not true. Under this interpretation the JTB definition of knowledge survives. The problem is now not to define knowledge but to define justification.

However, most contemporary epistemologists accept Gettier's conclusion. Their responses to the Gettier problem, therefore, consist of trying to find alternate analyses of knowledge. They have struggled to discover and agree upon as a beginning any single notion of truth, or belief, or justifying which is wholly and obviously accepted. Since truth, belief, and justifying have yet been not singly each singularly defined, then justified true belief may be defined singly is a problematical proposition presently, or that be the purpose of Gettier's theses to confound. Gettier, for many years a professor at University of Massachusetts Amherst later also was interested in the epistemic logic of Hintikka, a Finnish philosopher at Boston University, who published Knowledge and Belief in 1962.
[2]

The most common direction for this sort of response to take is what might be called a "JTB+G" analysis: that is, an analysis based on finding some fourth condition — a "no-Gettier-problem" condition — which, when added to the conditions of justification, truth, and belief, will yield a set of necessary and jointly sufficient conditions.

Another response is that of Alvin Goldman (1967), who suggested the addition of a causal condition: a subject's belief is justified, for Goldman, only if the truth of a belief has caused the subject to have that belief (in the appropriate way); and for a justified true belief to count as knowledge, the subject must also be able to "correctly reconstruct" (mentally) that causal chain. Goldman's analysis would rule out Gettier cases in that Smith's beliefs are not caused by the truths of those beliefs; it is merely accidental that Smith's beliefs in the Gettier cases happen to be true, or that the prediction made by Smith: " The winner of the job will have 10 coins", on the basis of his putative belief, (see also bundling) came true in this one case. Goldman faces the difficulty, however, of giving a principled explanation of how an "appropriate" causal relationship differs from an "inappropriate" one (without the circular response of saying that the appropriate sort of causal relationship is the knowledge-producing one), or retreating to a position in which appeal is made weakly to the notion of justified true belief being definable as by the consensus of learned opinion, which is useful, but not a fixed for all time unchanging definition as one would wish for as of similar reliability and utility as such purely scientific or physical definitions as that of momentum, or extension. Thus, adopting a causal response to the Gettier problem usually requires one to adopt (as Goldman gladly does) some form of reliabilism about justification. See Goldmans Theory of justification.

Omar dies of a heart attack. Later a madman decapitates Omar. Kasim comes along, sees Omar's detached head and immediately infers that Omar is dead.

By the justified true belief analysis, this is knowledge. Kasim's belief is true, and justified. But according to Goldman, Kasim's belief is not appropriately causally related to Omar being dead, so it isn't knowledge.

Keith Lehrer and Thomas Paxson (1969) proposed another attractive response, by adding a defeasibility condition to the JTB analysis. On their account, knowledge is undefeated justified true belief — which is to say that a justified true belief counts as knowledge if and only if it is also the case that there is no further truth that, had the subject known it, would have defeated her present justification for the belief. (Thus, for example, Smith's justification for believing that the person who will get the job has ten coins in his pocket is his justified belief that Jones will get the job, combined with his justified belief that Jones has ten coins in his pocket. But if Smith had known the truth that Jones will not get the job, that would have defeated the justification for his belief.) However, many critics (such as Marshall Swain [1974]) have argued that the notion of a defeater fact cannot be made precise enough to rule out the Gettier cases without also ruling out legitimate cases of knowledge. And, is Smith's justification for believing (in the sentence above) his "reasoning why he believes" or "the reasons on which he relies, when believing"? In what degree of exactitude , in discussing this counterexample, case (I), and in what precise mode of speech is it possible to speak of Smith having a justified true belief in case (I) on only a single occasion, this exposition by the writer of the particular form of words (case(I)), this simulated thought experiment, in words concerning Smith?

Pragmatism, or the science of pragmatics was developed as a philosophical doctrine by chiefly C.S.Peirce and William James (1842-1910). James' epistomological model of truth was that which works in the way of belief, and a belief was true if in the long run it worked for all of us, and guided us expeditiously through our semihospitable world.
Peirce argued that metaphysics could be set aside in favour of a pragmatic approach. "Consider what, effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object."
From a pragmatic viewpoint then, defining on a particular occasion whether a particular belief can rightly be said to be both true and justified is seen as no more than an exercise in pedantry, but being able to discern whether that belief led to fruitful outcomes is a fruitful enterprise.

The difficulties involved in producing a viable fourth condition have led to claims that attempting to repair the JTB account is a deficient strategy. For example, one might argue that what the Gettier problem shows is not the need for a fourth independent condition in addition to the original three, but rather that the attempt to build up an account of knowledging by conjoining a set of independent conditions was misguided from the outset. Those who have adopted this approach generally argue that epistemological terms like justification, evidence, certainty, etc. should be analyzed in terms of a primitive notion of knowledge, rather than vice versa. Knowledge is understood as factive, that is, as embodying a sort of epistemological "tie" between a truth and a belief. The JTB account is then criticized for trying to get and encapsulate the factivity of knowledge "on the cheap," as it were, or via a circular argument, by replacing an irreducible notion of factivity with the conjunction of some of the properties that accompany it (in particular, truth and justification). Of course, the introduction of irreducible primitives into a philosophical theory is always problematical (some would say a sign of desperation), and such anti-reductionist accounts are unlikely to please those who have other reasons to hold fast to the method behind JTB+G accounts. The wish to retain a formalised construction for JTB is an intuitive one, and led to Poincare, considered a pre-intuitivist in relation to the school of intuitionism associated with Brouwer, calling into question the Law of the excluded middle, held to formally, by Hilbert.

Fred Dretske (1971) developed an account of knowledge which he called "conclusive reasons", revived by Robert Nozick as what he called the subjunctive or truth-tracking account. (1981) Nozick's formulation posits that proposition P is an instance of knowledge when:

p is true

S believes that p

if p were true, S would believe that p

if p weren't true, S wouldn't believe that p

Nozick's definition is intended to preserve Goldman's intuition that Gettier cases should be ruled out by disacknowledging "accidentally" true justified beliefs, but without risking the potentially onerous consequences of building a causal requirement into the analysis. This tactic though, invites the reposte that Nozick's account merely hides the problem and does not solve it, for it leaves open the question of why Smith would not have had his belief if it had been false. The most promising answer seems to be that it is because Smith's belief was caused by the truth of what he believes; but that puts us back in the causalist camp.

Criticisms and counter examples (notably the Grandma case) prompted a revision, which resulted in the alteration of (3) and (4) to limit themselves to the same method (i.e. vision):

p is true

S believes that p

if p were true, S (using M) would believe that p

if p weren't true, S (using method M) wouldn't believe that p

That this view though remains problematical has been pointed out in a lecture by Saul Kripke. The counterexample he uses is called the Fake Barn Country example, which explains that in a certain locality are a number of fake barns or facades of barns. In the midst of these fake barns is one real barn, which is painted red. There is one piece of crucial information for this example: the fake barns cannot be painted red.

Jones is driving along the highway, looks up and happens to see the real barn, and so forms the belief

I see a barn

Though Jones has gotten lucky, he could have just as easily been deceived and not have known it. Therefore it doesn't fulfill premise 4, for if Jones saw a fake barn he wouldn't have any idea it was a fake barn. So this is not knowledge.

An alternate example is if Jones looks up and forms the belief

I see a red barn.

According to Nozick's view this fulfills all four premises. Therefore this is knowledge, since Jones couldn't have been wrong, since the fake barns cannot be painted red. This is a troubling account however, since it seems the first statement I see a barn can be inferred from I see a red barn, however by Nozick's view the first belief is not knowledge and the second is knowledge.

Richard Kirkham has proposed that we start with a definition of knowledge so strong that a counterexample to it is logically impossible. Then we see if there is any way that it can be weakened without becoming subject to a counterexample. He concludes that there will always be a counterexample to any definition of knowledge that does not require that the believer's evidence logically necessitates the truth of the belief. Since any such definition would entail that almost nothing is known by anyone, Kirkham embraces scepticism about knowledge, or there is skepticism as to the precision with which a definition can be advanced of knowledge. So he notes that just because the word "knowledge" cannot be applied to much of anything, it does not follow that beliefs cannot be rational at all. (see also: fallibilism)

One could turn the tables on Smith and the Gettier analysis by retreating then from the strong position in stages, and holding to that weakened form which can count as superior for some cogent purpose or in an intuititive way to the Gettier analysis in the case of any particular exemplar. One would advance a series of say ten or more distinct lines of deflecting the Gettier analysis, each on linguistic, or even metaepistemological (in this case, the issue of Smith's identity) grounds, since the Gettier analysis is faultless in logic

One might respond to Gettier by finding a way to avoid his conclusion(s) in the first place. However, it can hardly be argued that knowledge is justified true belief if there are cases that are justified true belief without being knowledge; thus, those who want to avoid Gettier's conclusions have to find some way to defuse Gettier's counterexamples. In order to do so, within the parameters of the particular counter-example or exemplar, they must then either accept

that Gettier's cases are not really cases of justified true belief or

that Gettier's cases really are cases of knowledge after all

or) demonstrate a case in which it is possible to circumvent surrender to the exemplar by eliminating any necessity for it to be considered that JTB apply in just those areas which Gettier has rendered obscure, without thereby lessening the force of JTB to apply in those cases where it actually is crucial.
Then though Gettier's cases stipulate that Smith has a certain belief and that his belief is true, it seems that in order to propose (1), one must argue that Gettier, (or, that is, the writer responsible for the particular form of words on this present occasion known as case (1), and who makes assertion's about Smith's "putative" beliefs), goes wrong because he has the wrong notion of justification. Such an argument often depends on an externalist account on which "justification" is understood in such a way that whether or not a belief is "justified" depends not just on the internal state of the believer, but also on how that internal state is related to the outside world. Externalist accounts typically are constructed such that Smith's putative beliefs in Case I and Case II are not really justified (even though it seems to Smith that they are), because his beliefs are not lined up with the world in the right way, or that it is possible to show that it is invalid to assert that "Smith" has any significant particular" belief at all, in terms of JTB or otherwise. Such accounts, of course, face the same burden as causalist responses to Gettier: they have to explain what sort of relationship between the world and the believer counts as a justificatory relationship.

Those who accept (2) are by far in the minority in Anglo-American philosophy; generally those who are willing to accept it are those who have independent reasons to say that more things count as knowledge than the intuitions that led to the JTB account would acknowledge. Chief among these are epistemic minimalists such as Crispin Sartwell, who hold that all true belief, including both Gettier's cases and lucky guesses, counts as knowledge.